IEEE TRANSACTIONS ON BROADCASTING, VOL. 46, NO. 3, SEPTEMBER 2000 227
A Quadrature Baseband Approach to Direct Digital FM
Synthesis
G.-J. van Rooyen and J. G. Lourens
Abstract—The use of direct digital synthesis (DDS) to synthesize high-
frequency analog signals has received much attention over the past decade.
This technique allows modulation schemes such as FM and PM to be im-
plemented with high fidelity using digital components. This paper inves-
tigates an improvement on the typical DDS approach of synthesizing the
desired signal at an intermediate frequency. Instead, two quadrature base-
band signals are generated, which are then mixed directly to the output
center frequency. This method can be used to synthesize FM signals of ar-
bitrarily high output frequency, using digital circuitry with considerably
lower clock speeds.
I. INTRODUCTION
Much has been written on the subject of direct digital synthesis
(DDS) in recent years [8], [9], [3], [4]. Modulation techniques that
were once the sole domain of analog electronics can now easily be
implemented using digital signal processors or FPGAs. Although the
basic concept was formulated almost two decades ago [5], it was only
during the 1990s that the state of the art in IC performance allowed
widespread implementation of DDS at broadcast frequencies [9], [7].
A practical use of DDS is found in the generation of frequency mod-
ulated (FM) signals, especially to generate highly linear broadcast sig-
nals. An improved signal to noise ratio (SNR) is also possible when
digital synthesis is used [4], [7], [8].
The digital calculation of an output signal is limited by the clock
speed of the ICs that are used. Although the calculation speed of dig-
ital components is constantly improving, the typical output sampling
rate that can be achieved might be much lower than the desired FM
broadcast frequency. The usual solution to this problem, both in litera-
ture and in practice, is to synthesize an FM signal at a lower frequency,
within the capability of the employed ICs. This intermediate signal is
then upconverted to the required broadcast frequency [8]. The theory
behind this technique will be summarized in the next section. Conse-
quently, certain inherent shortcomings in this method will be pointed
out.
As will be illustrated in Section III, the disadvantages of using an
intermediate frequency can be overcome by using a technique that de-
composes the FM signal into two quadrature components in the base-
band. This allows an output sampling rate dependent only on the max-
imum FM frequency deviation. Such a lower sampling rate can have
significant advantages, as will be shown in Section III-C.
II. HIGH-FREQUENCY DDS
A. Overview
The standard approach to DDS is to digitally sculpt the desired
analog signal around a chosen carrier frequency. The reader is referred
to the paper by Twitchell [8] for a fuller analysis of this technique;
several tutorials can also be recommended [3], [4], [6].
In analog FM modulation, the phase angle at any instant t is given
by
(t) = !
c
t+ k
f
t
0
m()d + 
o
(1)
Manuscript received November 9, 1999; revised August 4, 2000.
The authors are with the Deparment of Electrical and Electronic Engineering,
Stellenbosch University (e-mail: g-j@ieee.org; lourens@firga.sun.ac.za).
Publisher Item Identifier S 0018-9316(00)11526-4.
where
!
c
is the carrier frequency,
k
f
is the deviation constant,
m(t) is the modulating signal, and

o
represents the phase angle at time t = 0.
If modulation is to be performed in discrete time on a sampled signal,
equation (1) can be rewritten as
(nT ) = nTF
c
+ T
n
k=1
m(kT ) + 
o
(2)
In this equation, T is the sampling interval and n is the sample
number. F
c
is a constant that determines the carrier frequency of the
discrete-time output signal. If each output sample from equation (2)
is used as the phase index to a sine lookup-table, a sampled FM
signal will result. Under the assumption that all significant frequency
components are below the Nyquist limit, an analog FM signal can be
produced by lowpass filtering the sampled FM signal. Theoretically,
the resultant analog signal will be identical to the one produced using
an ideal analog FM modulator [as described by equation (1)].
Fig. 1 shows a block diagram of the direct digital FM synthesizer
described by equation (2). The system is synchronized to a clock with
a period equal to the sampling interval, T . During each cycle, a sam-
pled input value is added to the phase accumulator. The input samples
must be offset with a positive constantF
c
to ensure that the phase accu-
mulator is always incremented by a positive value. Consequently, the
phase accumulator performs large phase increments for high values of
the modulation signal, and smaller phase increments for low values of
the modulation signal. When the modulation signal is zero, the phase
accumulator increments at a rate determined by F
c
alone.
When the value of the phase accumulator grows so large that it is
incremented beyond the maximum value allowed by the architecture,
an overflow occurs. This overflow can be ignored by the hardware, and
the remainder taken as the new phase value. This represents the phase
moving through 2 radians.
The phase accumulator is next used as an index to a sine lookup table,
producing a discrete-time version of the desired FM signal. By per-
forming digital-to-analog conversion and lowpass-filtering, the analog
FM signal is produced.
B. Inherent Problems
FM signals must often be broadcast at frequencies much higher than
the sampling frequency attainable by the digital circuitry. As was al-
ready noted, the usual solution to this problem is to generate the DDS
FM signal at an intermediate frequency, within the capacity of the dig-
ital components. This intermediate signal is then mixed to the desired
broadcast frequency, and alias components are filtered.
If the intermediate output carrier frequency is much lower than the
broadcast frequency, upmixing results in alias components that lie very
close to the desired components in the frequency spectrum. The fil-
tering of these unwanted frequencies can become a very demanding
task, and several stages of mixing and filtering might be required.
For example, if an intermediate signal is generated at 5 MHz and
must be broadcast at 100 MHz, single-stage upmixing results in alias
signals at 95 MHz and 105 Mhz. Even if the signal bandwidth is neg-
ligibly small, a filter with a quality factor of at least 10 is required to
suppress these alias signals by only 3 dB. Stronger suppression (es-
pecially when the signal bandwidth is not negligible) could demand a
much higher quality factor. An obvious disadvantage is the increase in
system cost and complexity. For this reason, it is desirable to generate
as high an intermediate output frequency as possible.
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